Was it produced by the state and given to soldiers, or was it made privately and sold on the open market? Was it a mix?
In Land and Privilege in Byzantium I found this passage: A few Byzantine writers protested over the confiscation of monastic property. In the second half of the fourteenth century Nicholas Kavasilas, in his Discourse Concerning Illegal Acts of Officials against Things Sacred, addressed the issue of the confiscation of monastic land for military ends. He wrote that his opponents would argue, among other things, that such confiscations were justifiable because “we arm soldiers from these things.” Similarly, in 1383 Isidore, the metropolitan of Thessaloniki, complained that church property which belonged to his see in Thessaloniki was threatened with confiscation for military ends.
Does that mean to imply that the state was providing equipment for the military? Was that a usual occurrence or an emergency measure?
Sorry this is late, it has been a busy few days at work.
The Roman state from the principate all the way to roughly the 9th century AD was responsible, in some way or another, for equipping its soldiers. This took multiple forms but two are most relevant to the Byzantine period of Roman history: arms produced in the Roman State's factories and provided to the soldiers, and the cash equivalent for soldiers to buy the appropriate arms and uniforms at their discretion. Despite providing a cash allowance for the purchase of equipment, the arms were still considered to be owned by the state. This is clear legally, and also based on the Roman State's policy of replacing weapons lost or damaged while on duty. This policy swung back and forth through Byzantine history, typically state provided arms during poor economic circumstances, and cash allowances during prosperous times. Anastasias I instituted a generous cash allowance, proving extremely popular with the army. Maurice Tiberius attempted several times to move back to a state backed central distribution of arms and equipment instead of the cash allotment. This was unpopular and caused multiple mutinies. It is likely that during Heraclius reign that equipment was state provisioned again to save money in addition to army pay cuts.
During the post Heraclian period or middle Byzantine period, state officials called Kommerkiarioi were largely responsible for the transport and distribution of arms to soldiers across the Empire. The Kommerkiarios (κομμερκιαριος) is a frankly bizarre position in the Byzantine administration who's responsibilities were initially related to the collection of customs at border crossings. Later on this evolved from border customs to general duty collection on various goods, inspecting important and exports, (they may have also sold slaves at certain points, particularly the 7th century). The Kommerkarios were also involved in the state monopoly on Silk at one point. Regarding the Kommerkiarioi and their relation to the military, they held offices for a set period, usually a few years, in a set geographical region, and operated an apothekai or warehouse. These warehouses were used to distribute equipment, rations and other military supplies amongst the provinces. One possible explanation for how exactly this worked was that the Kommerkiarios purchased equipment from the state, either in Constantinople (less likely), state factories in the provinces (more likely) or from local private craftsmen (also likely), then used his district's apothekai as a centralized distribution center where local soldiers could acquire equipment or supplies by paying either in kind or in cash depending on the time period. The Kommerkarios was then able to keep some percentage of the profits.
As far as the manufacture of weapons and equipment, we have documentation of state factories or ergasteria (ἐργαστήριον) in Constantinople. For example, the Emperor Leo III established an armor factory complete with furnaces inside of a repurposed monastery. Presumably provincial factories also existed, in part to supply the apothekai, and also to supply campaigns. We have relatively detailed records of the Empire's campaign to Crete in the 10th century, these include Imperial demands of the strategos of the Thessalonica of 200,000 arrows, 3,000 spears and as many shields as could be produced. This would not have been possible without the presence of a local means of production.
Sources
Strategikon Maurice Tiberius
Praecepta Militaria Nikephoros Phokas
Recruitment and Conscription John Haldon
Military Service, Lands, and the Status of Soldiers John Haldon
Life of Saint Philaret the Merciful Dimitri of Rostov
De Ceremoniis Contantine VII
Byzantium and its Army Warren Treadgold
The Oxford Dictionary of Byzantium Alexander P. Kazhdan
Edit: missed a source